Our account of the Blind Spot is based on the work of two major philosophers and mathematicians, Edmund Husserl and Alfred North Whitehead. Husserl, the German thinker who founded the philosophical movement of phenomenology, argued that lived experience is the source of science. It’s absurd, in principle, to think that science can step outside it. The ‘life-world’ of human experience is the ‘grounding soil’ of science, and the existential and spiritual crisis of modern scientific culture – what we are calling the Blind Spot – comes from forgetting its primacy.

Whitehead, who taught at Harvard University from the 1920s, argued that science relies on a faith in the order of nature that can’t be justified by logic. That faith rests directly on our immediate experience. Whitehead’s so-called process philosophy is based on a rejection of the ‘bifurcation of nature’, which divides immediate experience into the dichotomies of mind versus body, and perception versus reality. Instead, he argued that what we call ‘reality’ is made up of evolving processes that are equally physical and experiential.

Nowhere is the materialistic bias in science more apparent than quantum physics, the science of atoms and subatomic particles. Atoms, conceived as the building blocks of matter, have been with us since the Greeks. The discoveries of the past 100 years would seem to be a vindication for all those who have argued for an atomist, and reductionist, conception of nature. But what the Greeks, Isaac Newton and 19th-century scientists meant by the thing called an ‘atom’, and what we mean today, are very different. In fact, it’s the very notion of a ‘thing’ that quantum mechanics calls into question.

The classic model for bits of matter involves little billiard balls, clumping together and jostling around in various forms and states. In quantum mechanics, however, matter has the characteristics of both particles and waves. There are also limits to the precision with which measurements can be made, and measurements seem to disturb the reality that experimenters are trying to size up.

Today, interpretations of quantum mechanics disagree about what matter is, and what our role is with respect to it. These differences concern the so-called ‘measurement problem’: how the wave function of the electron reduces from a superposition of several states to a single state upon observation. For several schools of thought, quantum physics doesn’t give us access to the way the world fundamentally is in itself. Rather, it only lets us grasp how matter behaves in relation to our interactions with it. — The Blind Spot of Science and the Neglect of Lived Experience

There is nothing "necessary" about 2 + 2 = 4. In fact this depends on a number of more basic assumptions (axioms). — EricH

It assumes God pre-exists matter, but God is something. — Relativist

To understand the development, one has to understand the intuitive rationality of animism, and the counterintuitive nature of the modern, dead world. One has to disabuse oneself of modernity. — unenlightened

The tremendously enlarged universe of modern cosmology is conceived as a field of inanimate masses and forces which operate according to the laws of inertia and of quantitative distribution in space. This denuded substratum of all reality could only be arrived at through a progressive expurgation of vital features from the physical record and through strict abstention from projecting into its image our own felt aliveness. In the process the ban on anthropomorphism was extended to zoomorphism in general. What remained is the residue of the reduction toward the properties of mere extension which submit to measurement and hence to mathematics. These properties alone satisfy the requirements of what is now called exact knowledge: and representing the only knowable aspect of nature they, by a tempting substitution, came to be regarded as its essential aspect too: and if this, then as the only real in reality.

This means that the lifeless has become the knowable par excellence and is for that reason also considered the true and only foundation of reality. It is the "natural" as well as the original state of things. Not only in terms of relative quantity but also in terms of ontological genuineness, nonlife is the rule, life the puzzling exception in physical existence.

Accordingly, it is the existence of life within a mechanical universe which now calls for an explanation, and explanation has to be in terms of the lifeless. Left over as a borderline case in the homogeneous physical world-view, life has to be accounted for in the terms of that view. — Hans Jonas, The Phenomenon of Life:Towards a Philosophy of Biology

Something cannot come from nothing. — Clearbury

if something can come from nothing then there is no need to posit God. — Clearbury

You'd probably like Between Naturalism and Religion (2008) — J

Lots to be said about Nagel and religion. Is he really open to religious belief? — J

He wasn't there again today. Oh, how I wish he'd go away. — Banno

Here we are talking about Mathematics, and he must introduce god, but not in so many words. Moreover, he sees any objection to this unneeded insertion as further evidence of a supposed scientistic fear of religion. — Banno

… the apparent rejection or disappearance of religion and theology in fact conceals the continuing relevance of theological issues and commitments for the modern age. Viewed from this perspective, the process of secularization or disenchantment that has come to be seen as identical with modernity was in fact something different than it seemed, not the crushing victory of reason over infamy, to use Voltaire’s famous term, not the long drawn out death of God that Nietzsche proclaimed, and not the evermore distant withdrawal of the deus absconditus Heidegger points to, but the gradual transference of divine attributes to human beings (an infinite human will), the natural world (universal mechanical causality), social forces (the general will, the hidden hand), and history (the idea of progress, dialectical development, the cunning of reason). … — Reader Review

Mathematical platonism, otherwise known as realism, is just the view that mathematical objects are neither mental nor physical. We call them abstract objects. That's it. There's no accompanying doctrine. — frank

Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects that aren’t part of the causal and spatiotemporal order studied by the physical sciences.[1] Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate.

Although these philosophical consequences are not unique to mathematical platonism, this particular form of platonism is unusually well suited to support such consequences. For mathematics is a remarkably successful discipline, both in its own right and as a tool for other sciences.[2] Few contemporary analytic philosophers are willing to contradict any of the core claims of a discipline whose scientific credentials are as strong as those of mathematics (Lewis 1991, pp. 57–9). So if philosophical analysis revealed mathematics to have some strange and surprising consequences, it would be unattractive simply to reject mathematics.[3] A form of Platonism based on a discipline whose scientific credentials are less impressive than those of mathematics would not be in this fortunate situation. For instance, when theology turns out to have some strange and surprising philosophical consequences, many philosophers do not hesitate to reject the relevant parts of theology.

articulates a position that I think is broadly correct, but you can hold it and still be an atheist to the core. — J

Neoplatonic mathematics is governed by a fundamental distinction which is indeed inherent in Greek science in general, but is here most strongly formulated. According to this distinction, one branch of mathematics participates in the contemplation of that which is in no way subject to change, or to becoming and passing away. This branch contemplates that which is always such as it is and which alone is capable of being known: for that which is known in the act of knowing, being a communicable and teachable possession, must be something that is once and for all fixed — Jacob Klein, Greek Mathematical Thought and the Origin of Algebra

History of philosophy isn't my forte, and I defer to Nagel on this, though it does seem a little oversimplified? — J

The only form that genuine reasoning can take consists in seeing the validity of the arguments, in virtue of what they say. As soon as one tries to step outside of such thoughts, one loses contact with their true content. And one cannot be outside and inside them at the same time: If one thinks in logic, one cannot simultaneously regard those thoughts as mere psychological dispositions, however caused or however biologically grounded. If one decides that some of one's psychological dispositions are, as a contingent matter of fact, reliable methods of reaching the truth (as one may with perception, for example), then in doing so one must rely on other thoughts that one actually thinks, without regarding them as mere dispositions. One cannot embed all one's reasoning in a psychological theory, including the reasonings that have led to that psychological theory. The epistemological buck must stop somewhere. By this I mean not that there must be some premises that are forever unrevisable but, rather, that in any process of reasoning or argument there must be some thoughts that one simply thinks from the inside--rather than thinking of them as biologically programmed dispositions. — Thomas Nagel op cit

How is sex an external representation of a mind disassociating with itself? — Bob Ross

In Bernardo Kastrup’s framework, dissociated alters are conceptualized as individual living organisms, including humans, which are distinct expressions or manifestations of a single, overarching cosmic consciousness. According to this idealist ontology, there exists only one cosmic consciousness, and all living beings are dissociated alters of this consciousness. These alters are surrounded by the thoughts of cosmic consciousness, and the inanimate world we perceive is the extrinsic appearance of these thoughts. Living organisms, including humans, are the extrinsic appearances of other dissociated alters. This framework suggests that our subjective experiences and perceptions are localized within these dissociated alters, which are essentially segments of the broader cosmic consciousness.

Is there such a thing as health? Of course there is. Can you see it? Of course not. This does not mean that the forms are occult entities floating ‘somewhere else’ in ‘another world,’ a ‘Platonic heaven.’ It simply says that the intelligible identities which are the reality, the whatness, of things (such as "health") are not themselves physical things to be perceived by the senses, but must be grasped by thought.

It is in this sense, too, that Plato’s references to the forms as ‘patterns’ or ‘paradigms’, of which instances are ‘images,’ must be understood. All too often, ‘paradigm’ is taken to mean ‘model to be copied.’ The following has been offered as an example of this meaning of παράδειγμα (parádeigma) in classical Greek: “[T]he architect of a temple requiring, say, twenty-four Corinthian capitals would have one made to his own specifications, then instruct his masons to produce twenty-three more just like it.” Such a model is itself one of the instances: when we have the original and the twenty-three copies, we have twenty-four capitals of the same kind. It is the interpretation of forms as paradigms in this sense that leads to the ‘third man argument’ by regarding the form as another instance and the remaining instances as ‘copies’ of the form. This interpretation of Plato’s ‘paradigmatism’ reflects a pictorial imagination of the forms as, so to speak, higher-order sensibles located in ‘another world,’ rather than as the very intelligible identities, the whatnesses, of sensible things.

But forms cannot be paradigms in this sense. Just as the intelligible ‘look’ that is common to many things of the same kind, a form, as we have seen, is not an additional thing of that kind. Likewise, it makes no sense to say that a body, a physical, sensible thing, is a copy, in the sense of a replica or duplicate, of an intelligible idea. Indeed, Plato expressly distinguishes between a copy and an image: “Would there be two things, that is, Cratylus and an image of Cratylus, if some God copied not only your color and shape, as painters do, but also … all the things you have? — Eric D Perl Thinking Being, p31 ff

a platonic realm — Banno

The key difference between Frege and Popper here is...whether the 3rd realm exists independently of human thought, or is created by our thought. If Burge is right, then there's no doubt what Frege believed: complete independence. Popper stakes out a middle ground — J

Frege believed that number is real in the sense that it is quite independent of thought: 'thought content exists independently of thinking "in the same way", he says "that a pencil exists independently of grasping it. Thought contents are true and bear their relations to one another (and presumably to what they are about) independently of anyone's thinking these thought contents - "just as a planet, even before anyone saw it, was in interaction with other planets." ' Furthermore in The Basic Laws of Arithmetic he says that 'the laws of truth are authoritative because of their timelessness: they "are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this, that they authority for our thought if it would attain to truth." — Tyler Burge

Intelligible objects must be independent of particular minds because they are common to all who think. In coming to grasp them, an individual mind does not alter them in any way, it cannot convert them into its exclusive possessions or transform them into parts of itself. Moreover, the mind discovers them rather than forming or constructing them, and its grasp of them can be more or less adequate. Augustine concludes from these observations that intelligible objects must exist independently of individual human minds. — Cambridge Companion to Augustine

We bring one and two into existence, by and intentional act - it's something we do. — Banno

The only end of science, as such, is to learn the lesson that the universe has to teach it. In Induction it simply surrenders itself to the force of facts. But it finds . . . that this is not enough. It is driven in desperation to call upon its inward sympathy with nature, its instinct for aid, just as we find Galileo at the dawn of modern science making his appeal to il lume naturale. . . . The value of Facts to it, lies only in this, that they belong to Nature; and nature is something great, and beautiful, and sacred, and eternal, and real - the object of its worship and its aspiration.

The soul's deeper parts can only be reached through its surface. In this way the eternal forms, that mathematics and philosophy and the other sciences make us acquainted with will, by slow percolation, gradually reach the very core of one's being, and will come to influence our lives; and this they will do, not because they involve truths of merely vital importance, but because they [are] ideal and eternal verities. — Evolutionary Naturalism and the Fear of Religion

Even without God, the idea of a natural sympathy between the deepest truths of nature and the deepest layers of the human mind, which can be exploited to allow gradual development of a truer and truer conception of reality, makes us more at home in the universe than is secularly comfortable.

If anyone is spending their holiday on TPF, poor devils, then Merry Christmas! — J

Perhaps the attempt to understand God in terms of rational principles is a misguided attempt to understand a God who is understood, to the extent he is understood, as willful. — Fooloso4

But the PSR says that everything has an explanation. — Clearbury

I am going to call that a ticketyboo. — Clearbury

Existence isn't a property; that would imply there are objects in the world that lack it - which is absurd. All objects in the world exist. — Relativist

• a state of things not yet realized
• a specific separate object of a representation,
• a general type of property that may or may not exist,
• an abstract quality,
• an experience, and so forth-just not that which is actually present.
• something missing, separate, and possibly nonexistent
• irrelevant when it comes to inanimate things, but a defining property of life and mind
• what is absent matters.
• a purpose not yet actualized,
• a quality of feeling, a functional value just discovered
• not just superimposed probable physical relationships
• each an intrinsically absent aspect of something present

Rather than the problem of an infinite regress, the problem is one of the limits of human reason. — Fooloso4

It's not in dispute that a necessarily existing thing exists and can't not. But if the PSR is true, then there will be an explanation of that. You haven't provided one, I think. — Clearbury

One has to disabuse oneself of modernity. — unenlightened

I think that is to greatly underestimate the intelligence and intellectual honesty of those you disagree with — Janus

number is real and materially instantiated in the diversity of forms given to our perceptions. — Janus

The nature of the particular contents therefore makes no difference at all. This fact, as rudimentary as it is incontestable, already rules out a certain class of views concerning the origination of the number concepts: namely, the ones which restrict those concepts to special content domains, e.g., that of physical contents.

Yet if decisions were made in the direction of these ideals, might not they be tending towards the ethical? — ENOAH

since you are always arguing that reality is entirely constructed by consciousness — Janus

We can maintain that mathematical objects are mind-independent, self-subsistent and in every sense real, and we can also explain how we are cognitively related to them: they are invariants in our experience consciousness

Mathemarical concepts for Husserl are no more ‘real’ than the spatial objects we interact with in the world. — Joshs

Physicists, probably more than anyone else in science, are obsessed with simplicity, unification and "naturalness," and not without reason, because this attitude has accompanied spectacular advances in physics over the past two centuries. But how philosophically justified is it? And how sustainable? I suppose that goes to the question of the proverbial "unreasonable effectiveness of mathematics." — SophistiCat

Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades.

The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

In his later Ideas for a Pure Phenomenology and Phenomenological Philosophy (1913), Husserl develops the method of eidetic variation. Eidetic variation consists of a series of mental acts that aim to grasp an invariant, ideal, non-sensory object that serves as a substrate to a range of experiences. The same object is given across this range of experience and we experience its self-samenesss. Husserl suggested that this method would serve to sharpen our conceptual grasp of ideal objects, and Tieszen argues that this method is in fact close to the actual procedure employed in modern geometry. In abstract sciences, Tieszen writes, "objectivity and invariance go hand in hand" (p. 89), and invariance is best understood as givenness. An ontology of abstract objects, then, should rest on the elements of Husserlian epistemology.

Husserl called his position "transcendental" phenomenology, and Tieszen makes sense of this by claiming that it can be seen as an extension of Kant's transcendental idealism. The act of cognition constitutes its content as objective. Once we recognize the distinctive givenness of essences in our experience, we can extend Kant's realism about empirical objects grounded in sensible intuition to a broader realism that encompasses objects grounded in categorial intuition, including mathematical objects.

The view is very much like what Kant has to say about empirical objects and empirical realism, except that now it is also applied to mathematical experience. On the object side of his analysis Husserl can still claim to be a kind of realist about mathematical objects, for mathematical objects are not our own ideas (p. 57f.).

This view, Tieszen points out, can preserve all the advantages of Platonism with none of its pitfalls. We can maintain that mathematical objects are mind-independent, self-subsistent and in every sense real, and we can also explain how we are cognitively related to them: they are invariants in our experience, given fulfillments of mathematical intentions. The evidence that justifies our mathematical knowledge is of the same kind as the evidence available for empirical knowledge claims: we are given these objects. And, since they are given, not subjectively constructed, fictionalism, conventionalism, and similar compromise views turn out to be unnecessarily permissive. The only twist we add to a Platonic realism is that ideal objects are transcendentally constituted.

We can evidently say, for example, that mathematical objects are mind-independent and unchanging, but now we always add that they are constituted in consciousness in this manner, or that they are constituted by consciousness as having this sense … . They are constituted in consciousness, nonarbitrarily, in such a way that it is unnecessary to their existence that there be expressions for them or that there ever be awareness of them. (p. 13).

I am of the view that inner as opposed to outer, objective aspects of 'reality' are important here in the tradition of human understanding. Science, similarly to religion may be embedded in mythic understanding. What do you think, especially in relation to the concept of myth? As far as I see it is a topic involving dialogue between ancient philosophy, as well as anthropological thinking and research. How may the development of ideas about 'gods' or one God be understood in the history of religion and philosophy? — Jack Cummins

In a nutshell, 'mathematical platonism' would suggest people have experienced these higher realities and found mathematics to be existing within them. — Tzeentch

During his Manichaean period Augustine’s attention had been focused on the external corporeal world. His thinking had consequently been bound by sensory experience: he could conceive only what he could form a sensory image of. Platonism, however, admonished him to abandon the corporeal world and turn inward, using the eye of his own rational soul. When he did so, he discovered an astonishing new realm. The incorporeality, immutability, and eternity that characterize purely intellectual thought are the clues that led Augustine, by stages, to the divine nature itself.

Augustine begins by establishing a hierarchy that sorts into general categories and ranks the natures that comprise the universe: existence, life, and understanding:

Therefore the nature that merely exists (and neither lives nor understands) ranks below the nature that not only exists but also lives (but does not understand) – the soul of the non-human animals is of this sort. This nature in turn ranks below the nature that at once exists, lives, and understands – for example, the rational mind of the human being. (lib. arb. 2.6.13)

His strategy will be to argue that there is a nature that ranks above the rational mind of the human being, a nature that he will identify as divine (lib. arb. 2.6.14, 2.15.39). In order to discover it, he ascends the hierarchy of natures, turning attention first from bodies (the first and lowest-ranking category in the hierarchy) to the soul (psuche, the nature constitutive of both the second and third categories), and then within his own soul from the sensory (found in both human beings and the non-human animals) to the rational: “a kind of head or eye of our soul ... which does not belong to the nature of non-human animals” (lib. arb. 2.6.13).11

Having ascended as far as reason – that which is highest in us – he focuses on reason’s distinctive perceptual capacities and the distinctive sorts of objects they put us in contact with, the objects of pure thought. By way of example, Evodius, Augustine’s interlocutor in the dialogue, first suggests that they consider “the structure and truth of number,” by which he means arithmetical facts and relationships of the sort expressed by such truths as “seven plus three equals ten” (lib. arb. 2.8.20–21). Augustine himself adds the example of the indivisible mathematical unit that is the foundation of all number. He later introduces into the discussion a collection of a priori evaluative and normative truths such as “wisdom should be diligently sought after,” “inferior things should be subjected to superior things,” and “what is eternal is better than what is temporal” (lib. arb. 2.10.28). He thinks of these truths as constitutive of wisdom itself and therefore normative for anyone who would possess it. Moreover, anyone who is able to contemplate them will recognize their truth. Examination of these various examples leads Augustine to three conclusions: intelligible objects of these sorts are independent of our minds, incorporeal, and higher than reason. Put briefly, the main lines of his reasoning are as follows (lib. arb. 2.8.20–12.34):

1. Intelligible objects must be independent of particular minds because they are common to all who think. In coming to grasp them, an individual mind does not alter them in any way, it cannot convert them into its exclusive possessions or transform them into parts of itself. Moreover, the mind discovers them rather than forming or constructing them, and its grasp of them can be more or less adequate. Augustine concludes from these observations that intelligible objects must exist independently of individual human minds.

2. Intelligible objects must be incorporeal because they are eternal and immutable. By contrast, all corporeal objects, which we perceive by means of the bodily senses, are contingent and mutable. Moreover, certain intelligible objects – for example, the indivisible mathematical unit – clearly cannot be found in the corporeal world (since all bodies are extended, and hence divisible). These intelligible objects cannot therefore be perceived by means of the senses; they must be incorporeal and perceptible by reason alone.

3. Intelligible objects must be higher than reason because they judge reason. Augustine means by this that these intelligible objects constitute a normative standard against which our minds are measured (lib. arb. 2.5.12 and 2.12.34). We refer to mathematical objects and truths to judge whether or not and to what extent our minds understand mathematics. We consult the rules of wisdom to judge whether or not and to what extent a person is wise. In virtue of their normative relation to reason, Augustine argues that these intelligible objects must be higher than it, as a judge is higher than what it judges. Moreover, the intrinsic nature of these objects shows them to be higher than reason. They are eternal and immutable; by contrast, the human mind is clearly mutable. Augustine holds that since it is evident to all who consider it that the immutable is superior to the mutable (it is among the rules of wisdom he identifies), it follows that these objects are higher than reason.

...By focusing on objects perceptible by the mind alone and by observing their nature, in particular their eternity and immutability, Augustine came to see that certain things that clearly exist, namely, the objects of the intelligible realm, cannot be corporeal. When he cries out in the midst of his vision of the divine nature, “Is truth nothing just because it is not diffused through space, either finite or infinite?” (FVP 13–14), he is acknowledging that it is the discovery of intelligible truth that first frees him to comprehend incorporeal reality. — Cambridge Companion to Augustine

Popper's "Third world" differs from Plato's world of forms in that it is entirely an artefact of language and culture and is thus constantly changing. This is in contrast to the changeless world of Plato's forms. — Janus